The last that's heard of the fighter is that it was used to transport Obi-Wan from Utapau to the Sundered Heart.
But Obi-Wan Kenobi killed the Separatist general before he could get
away. After Obi-Wan was betrayed by his clone troops, he flew
Grievous’s fighter to a rendezvous with Bail Organa and Yoda.
Star Wars: Databack - The Soulless One
The ship receives a further mention in Star Wars: The Life and Legend of Obi-Wan Kenobi. Obi-Wan disposed of it at a spaceport en route to Tatooine. It's not entirely clear whether he sold it or simply abandoned it.
R2-D2 had been to the Lars family moisture farm just prior to the
Battle of Geonosis, and was able to provide the farm’s coordinates to
Obi-Wan. The starfighter that Obi-Wan had taken from the late General
Grievous had remained in Tantive IV’s docking bay, and Obi-Wan planned
to use the starfighter to take Luke to a spaceport at Nar Shaddaa, a
moon in a space sector controlled by the Hutts. As Obi-Wan carried
Luke into the starfighter’s cockpit, R2-D2 beeped a farewell message
to the Jedi. There was no point in Obi-Wan saying goodbye to C-3PO,
for Bail Organa had already taken the security precaution of having
the talkative protocol droid’s memory erased. Holding Luke
Skywalker’s swaddled form against his chest, Obi-Wan Kenobi sat in an
uncomfortable seat on a crowded, Tatooine-bound starcruiser. The Jedi
Master had little experience holding babies, but he did his best to
look comfortable with the child in his arms.
Bail Organa had provided a supply of untraceable credits for Obi-Wan
to pay for the journey to the sand planet. To further maintain
secrecy, Obi-Wan and Luke were traveling to Tatooine via an indirect
route starting from Nar Shaddaa on a series of public transports.
During a layover at a space station, Obi-Wan witnessed a group of
travelers at a HoloNet kiosk, watching a broadcast about recent events
on Coruscant. Obi-Wan had cringed when he saw a hologram of Emperor
Palpatine urging viewers to report anyone whom they suspected of being
a Jedi or having “supernatural powers.” Palpatine’s words had prompted
one traveler to remark, “Thank goodness those terrible Jedi were
Star Wars: The Life and Legend of Obi-Wan Kenobi
It makes a further appearance in the Star Wars Galaxies expansion pack "Rage of the Wookiees". Evidently it was recovered by N-K Necrosis from a secret Empire storeroom on Utapau and used by this character until his death. At that point the deed transfers to the player character.